The population of a species of plant in a field is modelled using the formula P=50e0.1tP = 50e^{0.1t}P=50e0.1t where t t\,t is the number of weeks since the population was first recorded.
Write down the number of plants when the population was first recorded.
Find the rate of increase in the population 10 weeks after the population was first recorded.
Find how many weeks it takes for the number of plants to exceed 300.
62 exam-style questions on AQA A Level Maths 1.9 F: Exponentials and logarithms, covering 1.9.1 Exponential functions and their graphs, 1.9.2 Gradient of e^kx (A-level only), 1.9.3 Logarithms as inverse functions, 1.9.4 Laws of logarithms, 1.9.5 Solving exponential equations, 1.9.6 Logarithmic graphs to estimate parameters (A-level only), and 1.9.7 Exponential growth and decay. Each one has a worked solution and a mark scheme showing where the marks go.